Classification of linear operators with minimal polynomial \( f(t) = (t-a)(t-b)\), \( a\neq b\), acting in filtered vector space (Q2782062)

The author proposes a solution of the problem on classification up to similarity of the linear operators \(\mathcal A\) with minimal polynomial \( f(t) = (t-a)(t-b)\), \( a\neq b\), acting in filtered space \( \overline U = (U_0,U_1,\dots,U_n)\). The filtered space in finite-dimensional case is understood as the space \( U = U_0 \) together with the subspaces \( U_1,\dots ,U_n\), \( n\geq 0\), such that \( U_0\supseteq U_1\leq \dots \supseteq U_n\). The problem is solved in the framework of classical linear algebra and allows to compute for each operator the corresponding canonical form.